Granted, the premise of this thread is that Islam spreads into Europe many centuries ago and OTL, including modern Turkey, is nearly irrelevant. But the posts here since my last entry confirmed the point I was stressing: as you move out of the Sahara and into more moderate climates, Islam remains compatible with a lifestyle we identify as more or less European.
Sure, alcoholic beverages with their dehydrating effect can be a real problem in the middle eastern climates; before modern food processing and refrigeration, parasites in pork can be a real problem in hot climates; and the Saudi Arabian dress code does mandate protection against windblown sand. And Europe is different.
But back to the issue of a different time line. Progress and the path to a modern world lie directly through the development of mathematics, science and industrialization.
The ancient Greeks developed geometry and math, then the progress stopped. The Romans used what they could, but did not advance the battery of knowledge. The early Christian church had little need for these skills, beyond the rules of thumb preserved by the Romans.
Then the Arabs studied the subject, developing a numeral system and the fundamentals of algebra. But at one point, the science would reach a plateau and change very little.
This is the point in history where the time line can change. The Catholic church was lukewarm on math and oppressive to science when it came to astronomy and physics. Islamic leaders would have no such prejudice. Conclusion: certain advancements would progress faster between 1000 and 1500. The knowledge base available to Newton (in a tolerant environment) would have spread much sooner. Navigators would have figured out the issue of circumnavigating the earth long before Magellan. Now, consider that consequence.